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As leaked extracts of her speech revealed early on Tuesday, May has said she rejects “partial membership of the European Union, associate membership of the European Union, or anything that leaves us half-in, half-out”.
However, during her live broadcast on Tuesday morning, May said her government will pursue "the greatest possible access to the single market through a new comprehensive, bold and ambitious free trade agreement with the EU.
"This agreement should allow for the freest possible trade in goods and services between the EU and UK," she said. "It should give British companies the maximum freedom to trade with and operate within EU markets and let EU business do the same in UK."
May stressed that what she is proposing does not mean membership of the EU because "being a member of the single market would mean complying with the EU rules and regulations and this would be like not leaving the EU at all".
A global Britain must be free to strike trade agreements with countries outside the EU
But she added that the trade deal Britain will be pushing for "may take in elements of single market arrangements in certain areas", on the export of cars and lorries, for example, or the provision of financial services across borders.
"It makes no sense to start again from scratch on these," she said.
Global markets
May put much emphasis on the freedom Britain now has to negotiate trade deals with countries outside the EU, naming China, Brazil and the Gulf states as countries that have already expressed an interest in making deals with Britain post-Brexit.
The prime minister said she would also like to work on future trade ties with New Zealand, India and the US, where president-elect Donald Trump has already said he would prioritise a deal with the UK.
"A global Britain must be free to strike trade agreements with countries outside the EU, because although our trade with the EU is important, it is clear we need to significantly increase our trade with the fastest growing export markets in the world," the prime minister said, adding that trade as a percentage of GDP has broadly stagnated in the UK since it became a member of the EU.
Customs union
May added that she wants cross-border trade to be as "friction-free" as possible.
"I don't want the UK to be part of the common commercial policy or be bound by the common external tariff," she said, "but I do want us to have a customs agreement with the EU - whether that means we must reach a completely new customs agreement or become an associate member or remain a signatory to some members of it. I have an open mind on how we do it. It is not the means that matter but the ends and those ends are clear: I want to remove as many barriers to trade as possible."
Common travel area
In her only specific nod to Ireland, May said that maintaining the common travel area with the Republic of Ireland will be an important part of the negotiations, referring to the "family ties and bonds of affection" between our two countries.
"Nobody wants to return to the borders of the past - so we will try to work on a practical solution to ensure that common travel area as soon as we can," she said.
Certainty in the negotiations
May added that the British government will aim to provide "certainty" whenever it can throughout the negotiations: "There will be give and take so it is important to provide everybody with as much certainty as possible - that is why we gave certainty about farm payments soon after the referendum vote on 23 June."
The British people do not want to see an unravelling of the EU
The prime minister also said the government will put the final deal between Britain and EU to a vote in both houses of parliaments before it comes into force.
She added that 23 June was the moment the UK chose to build "a truly global Britain" and the reasons the British people made this decision were not understood by everybody in Europe.
But she stressed that the vote does not mean the British people want to see an "unravelling of the EU. It remains in our national interest that the EU should succeed," she said.
May added that the EU should not seek to punish Britain post-Brexit: "You don't want to make farmers and fishermen poor to make a point", she said.
The euro is currently trading at 0.87p, not having moved much since May's comments to Sky News about leaving the single market last Sunday.
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